Geometry and Convergence Analysis of Algorithms for Registration of 3D Shapes.
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| Title: | Geometry and Convergence Analysis of Algorithms for Registration of 3D Shapes. |
|---|---|
| Authors: | Pottmann, Helmut1 pottmann@geometrie.tuwien.ac.at, Huang, Qi-Xing2, Yang, Yong-Liang2, Hu, Shi-Min2 shimin@tsinghua.edu.cn |
| Source: | International Journal of Computer Vision. May2006, Vol. 67 Issue 3, p277-296. 20p. 3 Diagrams, 3 Charts, 5 Graphs. |
| Subjects: | Contact transformations, Geometry, Mathematical optimization, Program transformation, Structural optimization, Algorithms, Evolutionary computation, Stiff computation (Differential equations) |
| Abstract: | The computation of a rigid body transformation which optimally aligns a set of measurement points with a surface and related registration problems are studied from the viewpoint of geometry and optimization. We provide a convergence analysis for widely used registration algorithms such as ICP, using either closest points (Besl and McKay, 1992) or tangent planes at closest points (Chen and Medioni, 1991) and for a recently developed approach based on quadratic approximants of the squared distance function (Pottmann et al., 2004). ICP based on closest points exhibits local linear convergence only. Its counterpart which minimizes squared distances to the tangent planes at closest points is a Gauss–Newton iteration; it achieves local quadratic convergence for a zero residual problem and—if enhanced by regularization and step size control—comes close to quadratic convergence in many realistic scenarios. Quadratically convergent algorithms are based on the approach in (Pottmann et al., 2004). The theoretical results are supported by a number of experiments; there, we also compare the algorithms with respect to global convergence behavior, stability and running time. [ABSTRACT FROM AUTHOR] |
| Copyright of International Journal of Computer Vision is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Items | – Name: Title Label: Title Group: Ti Data: Geometry and Convergence Analysis of Algorithms for Registration of 3D Shapes. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Pottmann%2C+Helmut%22">Pottmann, Helmut</searchLink><relatesTo>1</relatesTo><i> pottmann@geometrie.tuwien.ac.at</i><br /><searchLink fieldCode="AR" term="%22Huang%2C+Qi-Xing%22">Huang, Qi-Xing</searchLink><relatesTo>2</relatesTo><br /><searchLink fieldCode="AR" term="%22Yang%2C+Yong-Liang%22">Yang, Yong-Liang</searchLink><relatesTo>2</relatesTo><br /><searchLink fieldCode="AR" term="%22Hu%2C+Shi-Min%22">Hu, Shi-Min</searchLink><relatesTo>2</relatesTo><i> shimin@tsinghua.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Computer+Vision%22">International Journal of Computer Vision</searchLink>. May2006, Vol. 67 Issue 3, p277-296. 20p. 3 Diagrams, 3 Charts, 5 Graphs. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Contact+transformations%22">Contact transformations</searchLink><br /><searchLink fieldCode="DE" term="%22Geometry%22">Geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Program+transformation%22">Program transformation</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+optimization%22">Structural optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Evolutionary+computation%22">Evolutionary computation</searchLink><br /><searchLink fieldCode="DE" term="%22Stiff+computation+%28Differential+equations%29%22">Stiff computation (Differential equations)</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The computation of a rigid body transformation which optimally aligns a set of measurement points with a surface and related registration problems are studied from the viewpoint of geometry and optimization. We provide a convergence analysis for widely used registration algorithms such as ICP, using either closest points (Besl and McKay, 1992) or tangent planes at closest points (Chen and Medioni, 1991) and for a recently developed approach based on quadratic approximants of the squared distance function (Pottmann et al., 2004). ICP based on closest points exhibits local linear convergence only. Its counterpart which minimizes squared distances to the tangent planes at closest points is a Gauss–Newton iteration; it achieves local quadratic convergence for a zero residual problem and—if enhanced by regularization and step size control—comes close to quadratic convergence in many realistic scenarios. Quadratically convergent algorithms are based on the approach in (Pottmann et al., 2004). The theoretical results are supported by a number of experiments; there, we also compare the algorithms with respect to global convergence behavior, stability and running time. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of International Journal of Computer Vision is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s11263-006-5167-2 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 20 StartPage: 277 Subjects: – SubjectFull: Contact transformations Type: general – SubjectFull: Geometry Type: general – SubjectFull: Mathematical optimization Type: general – SubjectFull: Program transformation Type: general – SubjectFull: Structural optimization Type: general – SubjectFull: Algorithms Type: general – SubjectFull: Evolutionary computation Type: general – SubjectFull: Stiff computation (Differential equations) Type: general Titles: – TitleFull: Geometry and Convergence Analysis of Algorithms for Registration of 3D Shapes. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Pottmann, Helmut – PersonEntity: Name: NameFull: Huang, Qi-Xing – PersonEntity: Name: NameFull: Yang, Yong-Liang – PersonEntity: Name: NameFull: Hu, Shi-Min IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 05 Text: May2006 Type: published Y: 2006 Identifiers: – Type: issn-print Value: 09205691 Numbering: – Type: volume Value: 67 – Type: issue Value: 3 Titles: – TitleFull: International Journal of Computer Vision Type: main |
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